RWM101: Foundations of Real World Math

In math, the additive identity is the name for a special number that does nothing when it is added to any other number. For real numbers, the number 0 plays this special role; this means that 0 is the additive identity for real numbers. In other words, the identity property of addition simply states that there is an additive identity called 0. This is probably a familiar fact for most of you. For example, $0+5=5$ or $0+(-7)=-7$.

It may seem strange to pay so much attention to such a simple or lazy number like 0. What is the big deal? It does nothing in addition. Why make such a fuss or give it a technical name?

As it turns out, paying careful attention to 0's special status early on will help you understand more complicated, unfamiliar numbers and objects. How about other operations? Do they feature a do nothing identity element? If we had not paid enough attention to 0 early on, this question would not have even occurred to us! But now we can ask, "does Average Joe's averaging operation have an identity" element?